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# Prove that if X and Y are independent standard normal ISBN: 9780131453401 223

## Solution for problem 8 Chapter 8.4

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Problem 8

Prove that if X and Y are independent standard normal random variables, then X + Y and X Y are independent random variables. This is a special case of the following important theorem. Let X and Y be independent random variables with a common distribution F. The random variables X + Y and X Y are independent if and only if F is a normal distribution function.

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##### ISBN: 9780131453401

Since the solution to 8 from 8.4 chapter was answered, more than 223 students have viewed the full step-by-step answer. Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. The full step-by-step solution to problem: 8 from chapter: 8.4 was answered by , our top Statistics solution expert on 01/05/18, 06:24PM. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3. The answer to “Prove that if X and Y are independent standard normal random variables, then X + Y and X Y are independent random variables. This is a special case of the following important theorem. Let X and Y be independent random variables with a common distribution F. The random variables X + Y and X Y are independent if and only if F is a normal distribution function.” is broken down into a number of easy to follow steps, and 67 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 59 chapters, and 1142 solutions.

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